<!DOCTYPE HTML>
<html lang="zh-CN">


<head>
    <meta charset="utf-8">
    <meta name="keywords" content="Matlab入门(二), 十二惊惶的gitee">
    <meta name="description" content="[TOC]
特殊矩阵：通用性矩阵：

以上函数调用格式相同，以zeros为例：

用于专门学科的特殊矩阵 (1)魔方矩阵Magic Squaren阶魔方阵由1,2,3,…,n2共n2个整数组成，且每行,每列以及主副对角线上各n个元素之和都相">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=no">
    <meta name="renderer" content="webkit|ie-stand|ie-comp">
    <meta name="mobile-web-app-capable" content="yes">
    <meta name="format-detection" content="telephone=no">
    <meta name="apple-mobile-web-app-capable" content="yes">
    <meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
    <meta name="referrer" content="no-referrer-when-downgrade">
    <!-- Global site tag (gtag.js) - Google Analytics -->


    <title>Matlab入门(二) | 十二惊惶的gitee</title>
    <link rel="icon" type="image/png" href="/shier_jinghuang/favicon.png">
    


    <!-- bg-cover style     -->



<link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/awesome/css/all.min.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/materialize/materialize.min.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/aos/aos.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/animate/animate.min.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/lightGallery/css/lightgallery.min.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/css/matery.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/css/my.css">
<link rel="stylesheet" type="text/css" href="/shier_jinghuang/css/dark.css" media="none" onload="if(media!='all')media='all'">




    <link rel="stylesheet" href="/shier_jinghuang/libs/tocbot/tocbot.css">
    <link rel="stylesheet" href="/shier_jinghuang/css/post.css">




    



    <script src="/shier_jinghuang/libs/jquery/jquery-3.6.0.min.js"></script>

<meta name="generator" content="Hexo 5.4.0"><link rel="alternate" href="/shier_jinghuang/atom.xml" title="十二惊惶的gitee" type="application/atom+xml">
</head>


<body>
    <header class="navbar-fixed">
    <nav id="headNav" class="bg-color nav-transparent">
        <div id="navContainer" class="nav-wrapper container">
            <div class="brand-logo">
                <a href="/shier_jinghuang/" class="waves-effect waves-light">
                    
                    <img src="/shier_jinghuang/medias/1.jpg" class="logo-img" alt="LOGO">
                    
                    <span class="logo-span">十二惊惶的gitee</span>
                </a>
            </div>
            

<a href="#" data-target="mobile-nav" class="sidenav-trigger button-collapse"><i class="fas fa-bars"></i></a>
<ul class="right nav-menu">
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/" class="waves-effect waves-light">
      
      <i class="fas fa-home" style="zoom: 0.6;"></i>
      
      <span>首页</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/tags" class="waves-effect waves-light">
      
      <i class="fas fa-tags" style="zoom: 0.6;"></i>
      
      <span>标签</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/categories" class="waves-effect waves-light">
      
      <i class="fas fa-bookmark" style="zoom: 0.6;"></i>
      
      <span>分类</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/archives" class="waves-effect waves-light">
      
      <i class="fas fa-archive" style="zoom: 0.6;"></i>
      
      <span>归档</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/about" class="waves-effect waves-light">
      
      <i class="fas fa-user-circle" style="zoom: 0.6;"></i>
      
      <span>关于</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/contact" class="waves-effect waves-light">
      
      <i class="fas fa-comments" style="zoom: 0.6;"></i>
      
      <span>留言板</span>
    </a>
    
  </li>
  
  <li class="hide-on-med-and-down nav-item">
    
    <a href="/shier_jinghuang/friends" class="waves-effect waves-light">
      
      <i class="fas fa-address-book" style="zoom: 0.6;"></i>
      
      <span>友情链接</span>
    </a>
    
  </li>
  
  <li>
    <a href="#searchModal" class="modal-trigger waves-effect waves-light">
      <i id="searchIcon" class="fas fa-search" title="搜索" style="zoom: 0.85;"></i>
    </a>
  </li>
  <li>
    <a href="javascript:;" class="waves-effect waves-light" onclick="switchNightMode()" title="深色/浅色模式" >
      <i id="sum-moon-icon" class="fas fa-sun" style="zoom: 0.85;"></i>
    </a>
  </li>
</ul>


<div id="mobile-nav" class="side-nav sidenav">

    <div class="mobile-head bg-color">
        
        <img src="/shier_jinghuang/medias/1.jpg" class="logo-img circle responsive-img">
        
        <div class="logo-name">十二惊惶的gitee</div>
        <div class="logo-desc">
            
            犁牛之子骍且角，虽欲勿用，山川其舍诸
            
        </div>
    </div>

    <ul class="menu-list mobile-menu-list">
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-home"></i>
			
			首页
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/tags" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-tags"></i>
			
			标签
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/categories" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-bookmark"></i>
			
			分类
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/archives" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-archive"></i>
			
			归档
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/about" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-user-circle"></i>
			
			关于
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/contact" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-comments"></i>
			
			留言板
		</a>
          
        </li>
        
        <li class="m-nav-item">
	  
		<a href="/shier_jinghuang/friends" class="waves-effect waves-light">
			
			    <i class="fa-fw fas fa-address-book"></i>
			
			友情链接
		</a>
          
        </li>
        
        
        <li><div class="divider"></div></li>
        <li>
            <a href="https://gitee.com/Im-so-scared-2/shier_jinghuang" class="waves-effect waves-light" target="_blank">
                <i class="fab fa-github-square fa-fw"></i>十二惊惶
            </a>
        </li>
        
    </ul>
</div>


        </div>

        
            <style>
    .nav-transparent .github-corner {
        display: none !important;
    }

    .github-corner {
        position: absolute;
        z-index: 10;
        top: 0;
        right: 0;
        border: 0;
        transform: scale(1.1);
    }

    .github-corner svg {
        color: #0f9d58;
        fill: #fff;
        height: 64px;
        width: 64px;
    }

    .github-corner:hover .octo-arm {
        animation: a 0.56s ease-in-out;
    }

    .github-corner .octo-arm {
        animation: none;
    }

    @keyframes a {
        0%,
        to {
            transform: rotate(0);
        }
        20%,
        60% {
            transform: rotate(-25deg);
        }
        40%,
        80% {
            transform: rotate(10deg);
        }
    }
</style>

<a href="https://gitee.com/Im-so-scared-2/shier_jinghuang" class="github-corner tooltipped hide-on-med-and-down" target="_blank"
   data-tooltip="十二惊惶" data-position="left" data-delay="50">
    <svg viewBox="0 0 250 250" aria-hidden="true">
        <path d="M0,0 L115,115 L130,115 L142,142 L250,250 L250,0 Z"></path>
        <path d="M128.3,109.0 C113.8,99.7 119.0,89.6 119.0,89.6 C122.0,82.7 120.5,78.6 120.5,78.6 C119.2,72.0 123.4,76.3 123.4,76.3 C127.3,80.9 125.5,87.3 125.5,87.3 C122.9,97.6 130.6,101.9 134.4,103.2"
              fill="currentColor" style="transform-origin: 130px 106px;" class="octo-arm"></path>
        <path d="M115.0,115.0 C114.9,115.1 118.7,116.5 119.8,115.4 L133.7,101.6 C136.9,99.2 139.9,98.4 142.2,98.6 C133.8,88.0 127.5,74.4 143.8,58.0 C148.5,53.4 154.0,51.2 159.7,51.0 C160.3,49.4 163.2,43.6 171.4,40.1 C171.4,40.1 176.1,42.5 178.8,56.2 C183.1,58.6 187.2,61.8 190.9,65.4 C194.5,69.0 197.7,73.2 200.1,77.6 C213.8,80.2 216.3,84.9 216.3,84.9 C212.7,93.1 206.9,96.0 205.4,96.6 C205.1,102.4 203.0,107.8 198.3,112.5 C181.9,128.9 168.3,122.5 157.7,114.1 C157.9,116.9 156.7,120.9 152.7,124.9 L141.0,136.5 C139.8,137.7 141.6,141.9 141.8,141.8 Z"
              fill="currentColor" class="octo-body"></path>
    </svg>
</a>
        
    </nav>

</header>

    



<div class="bg-cover pd-header post-cover" style="background-image: url('/shier_jinghuang/medias/featureimages/11.jpg')">
    <div class="container" style="right: 0px;left: 0px;">
        <div class="row">
            <div class="col s12 m12 l12">
                <div class="brand">
                    <h1 class="description center-align post-title">Matlab入门(二)</h1>
                </div>
            </div>
        </div>
    </div>
</div>




<main class="post-container content">

    
    <div class="row">
    <div id="main-content" class="col s12 m12 l9">
        <!-- 文章内容详情 -->
<div id="artDetail">
    <div class="card">
        <div class="card-content article-info">
            <div class="row tag-cate">
                <div class="col s7">
                    
                    <div class="article-tag">
                        
                            <a href="/shier_jinghuang/tags/%E5%AD%A6%E4%B9%A0%E8%AE%B0%E5%BD%95/">
                                <span class="chip bg-color">学习记录</span>
                            </a>
                        
                            <a href="/shier_jinghuang/tags/Matlab/">
                                <span class="chip bg-color">Matlab</span>
                            </a>
                        
                    </div>
                    
                </div>
                <div class="col s5 right-align">
                    
                    <div class="post-cate">
                        <i class="fas fa-bookmark fa-fw icon-category"></i>
                        
                            <a href="/shier_jinghuang/categories/%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/" class="post-category">
                                学习笔记
                            </a>
                        
                    </div>
                    
                </div>
            </div>

            <div class="post-info">
                
                <div class="post-date info-break-policy">
                    <i class="far fa-calendar-minus fa-fw"></i>发布日期:&nbsp;&nbsp;
                    2022-01-12
                </div>
                

                
                <div class="post-date info-break-policy">
                    <i class="far fa-calendar-check fa-fw"></i>更新日期:&nbsp;&nbsp;
                    2022-01-14
                </div>
                

                
                <div class="info-break-policy">
                    <i class="far fa-file-word fa-fw"></i>文章字数:&nbsp;&nbsp;
                    1.8k
                </div>
                

                
                <div class="info-break-policy">
                    <i class="far fa-clock fa-fw"></i>阅读时长:&nbsp;&nbsp;
                    6 分
                </div>
                

                
                    <div id="busuanzi_container_page_pv" class="info-break-policy">
                        <i class="far fa-eye fa-fw"></i>阅读次数:&nbsp;&nbsp;
                        <span id="busuanzi_value_page_pv"></span>
                    </div>
				
            </div>
        </div>
        <hr class="clearfix">

        
        <!-- 是否加载使用自带的 prismjs. -->
        <link rel="stylesheet" href="/shier_jinghuang/libs/prism/prism.min.css">
        

        

        <div class="card-content article-card-content">
            <div id="articleContent">
                <p>[TOC]</p>
<h2 id="特殊矩阵："><a href="#特殊矩阵：" class="headerlink" title="特殊矩阵："></a>特殊矩阵：</h2><p>通用性矩阵：</p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/6.png"></p>
<p>以上函数调用格式相同，以zeros为例：</p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/7.png"></p>
<h3 id="用于专门学科的特殊矩阵"><a href="#用于专门学科的特殊矩阵" class="headerlink" title="用于专门学科的特殊矩阵"></a>用于专门学科的特殊矩阵</h3><p> (1)魔方矩阵<strong>Magic Square</strong><br>n阶魔方阵由1,2,3,…,n2共n2个整数组成，且每行,每列以及主副对角线上各n个元素之和都相等。n阶魔方阵每行每列元素的和为**(1+2+3+…+ n^2)/n=(n+n^3)/2**。MATLAB函数magic(n)产生一个特定的魔方阵 </p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/8.png"></p>
<p>在<strong>MATLAB</strong>中，函数vander(V)生成以向量V为基础的范得蒙**(Vandermonde)**矩阵。</p>
<p>范德蒙矩阵常用于各种通信系统的纠错编码中，</p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/9.png"></p>
<p> 在MATLAB中，生成n阶希尔伯特矩阵的函数是hilb（n）</p>
<p>希尔伯特矩阵正定，且高度病态（即，任何一个元素发生一点变动，整个矩阵的行列式的值和逆矩阵都会发生巨大变化），病态程度和阶数相关。 </p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/10.png"></p>
<p>MATLAB生成伴随矩阵的函数是**compan(p)**，其中p是一个多项式的系数向量，高次幂系数排在前，低次幂系数排在后。</p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/11.png"></p>
<p>帕斯卡矩阵的第一行元素和第一列元素都为1，其余位置的元素是该元素的左边元素与上面元素相加，即P(i,j)=P(i,j- 1)+P(i-1,j)，且P(i,1)=1,P(1,j)=1。<strong>函数pascal(n)生成一个n阶帕斯卡矩阵。</strong></p>
<h2 id="矩阵变换"><a href="#矩阵变换" class="headerlink" title="矩阵变换"></a>矩阵变换</h2><h3 id="对角阵："><a href="#对角阵：" class="headerlink" title="对角阵："></a>对角阵：</h3><p>(1)<strong>对角矩阵：</strong>只有对角线上有非零元素的矩阵。</p>
<p>(2)<strong>数量矩阵：</strong>角线上元素相等的对角矩阵。</p>
<p>(3)<strong>单位矩阵：</strong>对角线上元素都为1的对角矩阵。</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">diag</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span>  <span class="token comment">%提取矩阵A主对角线元素，产生一个列向量</span>
<span class="token function">diag</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span>k<span class="token punctuation">)</span> <span class="token comment">%提取矩阵A第k条对角线的元素，产生一个列向量。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>

<p><strong>diag函数</strong>也可以构造对角矩阵：</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">diag</span><span class="token punctuation">(</span>V<span class="token punctuation">)</span> <span class="token comment">%一向量V为主对角线元素，产生对角矩阵。</span>
<span class="token function">diag</span><span class="token punctuation">(</span>V<span class="token punctuation">,</span>k<span class="token punctuation">)</span> <span class="token comment">%以向量V为第k条对角线元素，产生对角矩阵。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>

<h3 id="三角阵："><a href="#三角阵：" class="headerlink" title="三角阵："></a>三角阵：</h3><p>(1)上三角矩阵:</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">triu</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span>  <span class="token comment">%提取矩阵A的主对角线及以上的元素。</span>
<span class="token function">triu</span><span class="token punctuation">(</span>A<span class="token punctuation">,</span>k<span class="token punctuation">)</span><span class="token comment">%提取矩阵A的第k条对角线及以上的元素。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>

<p>(2)下三角矩阵：在MATLAB中，提取矩阵A的下三角矩阵的函数是tril，其用法与triu函数完全相同。</p>
<h3 id="矩阵的转置："><a href="#矩阵的转置：" class="headerlink" title="矩阵的转置："></a>矩阵的转置：</h3><p>转置运算符是小数点后面接单引号     <strong>.’</strong><br>共扼转置，其运算符是单引号 <strong>‘</strong> 它在转置的基础上还要取每个数的复共轲。 </p>
<h3 id="矩阵的翻转："><a href="#矩阵的翻转：" class="headerlink" title="矩阵的翻转："></a>矩阵的翻转：</h3><p><strong>rot90(A,k)</strong> :将矩阵A逆时针方向旋转90°的k倍，当k为1时可省略。 </p>
<p><strong>fliplr(A)</strong> :对矩阵A实施左右翻转。<strong>flipud(A)</strong> :对矩阵A实施上下翻转。</p>
<h3 id="矩阵的求逆："><a href="#矩阵的求逆：" class="headerlink" title="矩阵的求逆："></a>矩阵的求逆：</h3><p>对于一个方阵A，如果存在一个与其同阶的方阵B，使得AB=BA=l(I为单位矩阵)，则称B为A的逆矩阵，当然，A也是B的逆矩阵。**inv(A) ** :  求方阵A的逆矩阵。</p>
<h2 id="矩阵求值"><a href="#矩阵求值" class="headerlink" title="矩阵求值"></a>矩阵求值</h2><h3 id="矩阵的行列式"><a href="#矩阵的行列式" class="headerlink" title="矩阵的行列式"></a>矩阵的行列式</h3><p>把一个方阵看作一个行列式，并对其按行列式的规则求值，这个值就称为方阵所对应的行列式的值。<br>det(A):求方阵A所对应的行列式的值。</p>
<h3 id="矩阵的秩"><a href="#矩阵的秩" class="headerlink" title="矩阵的秩"></a>矩阵的秩</h3><p>矩阵线性无关的行数或列数称为矩阵的秩。rank(A):求矩阵A的秩。 </p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/12.png"></p>
<h3 id="矩阵的迹"><a href="#矩阵的迹" class="headerlink" title="矩阵的迹"></a>矩阵的迹</h3><p>矩阵的迹等于矩阵的对角线元素之和，也等于矩阵的特征值之和。</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">trace</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span>     <span class="token comment">%求矩阵A的迹。 </span><span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre>

<p><strong>向量和矩阵的范数：</strong>矩阵或向量的范数用来度量矩阵或向量在某种意义下的长度。</p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/13.png"></p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/14.png"></p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/15.png"></p>
<p> MATLAB提供了求3种矩阵范数的函数,其函数调用格式与求向量的范数的函数完全相同。</p>
<h3 id="矩阵的条件数"><a href="#矩阵的条件数" class="headerlink" title="矩阵的条件数"></a>矩阵的条件数</h3><p>矩阵A的条件数等于A的范数与A的逆矩阵的范数的乘积。条件数越接近于1，矩阵的性能越好，反之，矩阵的性能越差。</p>
<p>在MATLAB中，计算矩阵A的3种条件数的函数是:</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">cond</span><span class="token punctuation">(</span>A<span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span>          <span class="token comment">%计算A的1一范数下的条件数。</span>
<span class="token function">cond</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span>或<span class="token function">cond</span><span class="token punctuation">(</span>A<span class="token punctuation">,</span><span class="token number">2</span><span class="token punctuation">)</span> <span class="token comment">%计算A的2—范数下的条件数。</span>
<span class="token function">cond</span><span class="token punctuation">(</span>A<span class="token punctuation">,</span> <span class="token keyword">inf</span><span class="token punctuation">)</span>       <span class="token comment">%计算A的○o—范数下的条件数。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span></span></code></pre>

<h2 id="矩阵的特征值与特征向量"><a href="#矩阵的特征值与特征向量" class="headerlink" title="矩阵的特征值与特征向量"></a>矩阵的特征值与特征向量</h2><h3 id="矩阵特征值的数学定义"><a href="#矩阵特征值的数学定义" class="headerlink" title="矩阵特征值的数学定义"></a>矩阵特征值的数学定义</h3><p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/16.png"></p>
<h3 id="求矩阵的特征值和特征向量"><a href="#求矩阵的特征值和特征向量" class="headerlink" title="求矩阵的特征值和特征向量"></a>求矩阵的特征值和特征向量</h3><p>函数调用格式有两种：</p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab">E<span class="token operator">=</span><span class="token function">eig</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span> <span class="token comment">%求矩阵A的全部特征值，构成向量E</span>
<span class="token punctuation">[</span>X<span class="token punctuation">,</span>D<span class="token punctuation">]</span><span class="token operator">=</span><span class="token function">eig</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span> <span class="token comment">%求矩阵A的全部特征值，构成对角阵D，并产生矩阵X，X各列是相应的特征向量。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>

<h3 id="稀疏矩阵"><a href="#稀疏矩阵" class="headerlink" title="稀疏矩阵"></a>稀疏矩阵</h3><p>稀疏矩阵指的是零元素个数远远多于非零元素个数的矩阵，如果将大量的零元素也存储起来，必将导致存储空间的浪费。为此，MATLAB为稀疏矩阵提供特殊的存储方式。</p>
<h3 id="矩阵的存储方式"><a href="#矩阵的存储方式" class="headerlink" title="矩阵的存储方式"></a>矩阵的存储方式</h3><p>1,<strong>完全存储方式</strong></p>
<p>2,<strong>稀疏存储方式</strong>稀疏存储方式只存储矩阵的非零元素的值及其位置，即行号和列号。注意,采用稀疏存储方式时，矩阵元素的存储顺序并没有改变，也是按列的顺序进行存储。</p>
<h3 id="稀疏存储方式的产生"><a href="#稀疏存储方式的产生" class="headerlink" title="稀疏存储方式的产生"></a>稀疏存储方式的产生</h3><p>(1)<strong>完全存储方式与稀疏存储方式之间的转化</strong></p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab">A<span class="token operator">=</span>sparselS<span class="token punctuation">)</span>  <span class="token comment">%将矩阵S转化为稀疏存储方式的矩阵A。</span>
S<span class="token operator">=</span><span class="token function">full</span><span class="token punctuation">(</span>A<span class="token punctuation">)</span>    <span class="token comment">%将矩阵A转化为完全存储方式的矩阵S。</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span></span></code></pre>

<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/17.png"></p>
<p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/18.png"></p>
<p>用A的一行元素表示一个稀疏矩阵的元素，相当于A每一行的每个元素是相应的稀疏矩阵元素的一个信息。这些信息组合经过<code>spconvert</code>就可以得到相应的稀疏矩阵元素。</p>
<p>(3)<strong>带状稀疏矩阵的稀疏存储</strong><br>稀疏矩阵有两种基本类型:无规则结构的稀疏矩阵与有规则结构的稀疏矩阵。带状稀疏矩阵是指所有非零元素集中在对角线上的矩阵。<br>[B,d]=spdiags(A):从带状稀疏矩阵A中提取全部非零对角线元素赋给矩阵B及其这些非零对角线的位置向量d。<br>A=spdiags(B,d,m,n):产生带状稀疏矩阵的稀疏存储矩阵A，其中m、n为原带状稀疏矩阵的行数与列数，矩阵B的第i列即为原带状稀疏矩阵的第i条非零对角线，向量d为原带状稀疏矩阵所有非零对角线的位置。</p>
<p>(4)<strong>单位矩阵的稀疏矩阵</strong></p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab"><span class="token function">speye</span><span class="token punctuation">(</span>m<span class="token punctuation">,</span>n<span class="token punctuation">)</span>   <span class="token comment">%返回一个m*n的稀疏存储单位矩阵。</span><span aria-hidden="true" class="line-numbers-rows"><span></span></span></code></pre>

<h2 id="稀疏矩阵应用举例"><a href="#稀疏矩阵应用举例" class="headerlink" title="稀疏矩阵应用举例"></a>稀疏矩阵应用举例</h2><p><img src="https://shierjinghuang.github.io/2022/01/10/Matlab/19.png"></p>
<pre class="line-numbers language-matlab" data-language="matlab"><code class="language-matlab">clc<span class="token punctuation">;</span>clear
kf1<span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">2</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">0</span><span class="token punctuation">]</span><span class="token punctuation">;</span>     <span class="token comment">% 主对角线以下第一条元素</span>
k0 <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">2</span><span class="token punctuation">;</span><span class="token number">4</span><span class="token punctuation">;</span><span class="token number">6</span><span class="token punctuation">;</span><span class="token number">6</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>     <span class="token comment">% 主对角线元素</span>
k1 <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">;</span><span class="token number">3</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">4</span><span class="token punctuation">;</span><span class="token number">2</span><span class="token punctuation">]</span><span class="token punctuation">;</span>     <span class="token comment">% 主对角线以上第一条元素</span>
B <span class="token operator">=</span> <span class="token punctuation">[</span>kf1<span class="token punctuation">,</span>k0<span class="token punctuation">,</span>k1<span class="token punctuation">]</span><span class="token punctuation">;</span>
d <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token operator">-</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">0</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
A <span class="token operator">=</span> <span class="token function">spdiags</span><span class="token punctuation">(</span>B<span class="token punctuation">,</span>d<span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">,</span><span class="token number">5</span><span class="token punctuation">)</span><span class="token punctuation">;</span> <span class="token comment">% 产生稀疏存储的稀疏矩阵</span>
f <span class="token operator">=</span> <span class="token punctuation">[</span><span class="token number">0</span><span class="token punctuation">;</span><span class="token number">3</span><span class="token punctuation">;</span><span class="token number">2</span><span class="token punctuation">;</span><span class="token number">1</span><span class="token punctuation">;</span><span class="token number">5</span><span class="token punctuation">]</span><span class="token punctuation">;</span>
x <span class="token operator">=</span> A<span class="token operator">\</span>f               <span class="token comment">%求出解</span><span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>

<p>当参与运算的数据对象不全是稀疏储存矩阵时，所以结果是完全存储形式。</p>

                
            </div>
            <hr/>

            

    <div class="reprint" id="reprint-statement">
        
            <div class="reprint__author">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-user">
                        文章作者:
                    </i>
                </span>
                <span class="reprint-info">
                    <a href="/shier_jinghuang/about" rel="external nofollow noreferrer">十二惊惶</a>
                </span>
            </div>
            <div class="reprint__type">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-link">
                        文章链接:
                    </i>
                </span>
                <span class="reprint-info">
                    <a href="https://im-so-scared-2.gitee.io/shier_jinghuang/shier_jinghuang/2022/01/12/Matlab2/">https://im-so-scared-2.gitee.io/shier_jinghuang/shier_jinghuang/2022/01/12/Matlab2/</a>
                </span>
            </div>
            <div class="reprint__notice">
                <span class="reprint-meta" style="font-weight: bold;">
                    <i class="fas fa-copyright">
                        版权声明:
                    </i>
                </span>
                <span class="reprint-info">
                    本博客所有文章除特別声明外，均采用
                    <a href="https://creativecommons.org/licenses/by/4.0/deed.zh" rel="external nofollow noreferrer" target="_blank">CC BY 4.0</a>
                    许可协议。转载请注明来源
                    <a href="/shier_jinghuang/about" target="_blank">十二惊惶</a>
                    !
                </span>
            </div>
        
    </div>

    <script async defer>
      document.addEventListener("copy", function (e) {
        let toastHTML = '<span>复制成功，请遵循本文的转载规则</span><button class="btn-flat toast-action" onclick="navToReprintStatement()" style="font-size: smaller">查看</a>';
        M.toast({html: toastHTML})
      });

      function navToReprintStatement() {
        $("html, body").animate({scrollTop: $("#reprint-statement").offset().top - 80}, 800);
      }
    </script>



            <div class="tag_share" style="display: block;">
                <div class="post-meta__tag-list" style="display: inline-block;">
                    
                        <div class="article-tag">
                            
                                <a href="/shier_jinghuang/tags/%E5%AD%A6%E4%B9%A0%E8%AE%B0%E5%BD%95/">
                                    <span class="chip bg-color">学习记录</span>
                                </a>
                            
                                <a href="/shier_jinghuang/tags/Matlab/">
                                    <span class="chip bg-color">Matlab</span>
                                </a>
                            
                        </div>
                    
                </div>
                <div class="post_share" style="zoom: 80%; width: fit-content; display: inline-block; float: right; margin: -0.15rem 0;">
                    <link rel="stylesheet" type="text/css" href="/shier_jinghuang/libs/share/css/share.min.css">
<div id="article-share">

    
    <div class="social-share" data-sites="twitter,facebook,google,qq,qzone,wechat,weibo,douban,linkedin" data-wechat-qrcode-helper="<p>微信扫一扫即可分享！</p>"></div>
    <script src="/shier_jinghuang/libs/share/js/social-share.min.js"></script>
    

    

</div>

                </div>
            </div>
            
        </div>
    </div>

    

    

    

    

    

    

    

    

    

<article id="prenext-posts" class="prev-next articles">
    <div class="row article-row">
        
        <div class="article col s12 m6" data-aos="fade-up">
            <div class="article-badge left-badge text-color">
                <i class="fas fa-chevron-left"></i>&nbsp;上一篇</div>
            <div class="card">
                <a href="/shier_jinghuang/2022/01/12/Matlab%E4%B9%8B%E5%9B%BE%E5%83%8F%E7%BB%98%E5%88%B6/">
                    <div class="card-image">
                        
                        
                        <img src="/shier_jinghuang/medias/featureimages/11.jpg" class="responsive-img" alt="Matlab绘图">
                        
                        <span class="card-title">Matlab绘图</span>
                    </div>
                </a>
                <div class="card-content article-content">
                    <div class="summary block-with-text">
                        
                            
                        
                    </div>
                    <div class="publish-info">
                        <span class="publish-date">
                            <i class="far fa-clock fa-fw icon-date"></i>2022-01-12
                        </span>
                        <span class="publish-author">
                            
                            <i class="fas fa-bookmark fa-fw icon-category"></i>
                            
                            <a href="/shier_jinghuang/categories/%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/" class="post-category">
                                    学习笔记
                                </a>
                            
                            
                        </span>
                    </div>
                </div>
                
                <div class="card-action article-tags">
                    
                    <a href="/shier_jinghuang/tags/%E5%AD%A6%E4%B9%A0%E8%AE%B0%E5%BD%95/">
                        <span class="chip bg-color">学习记录</span>
                    </a>
                    
                    <a href="/shier_jinghuang/tags/Matlab/">
                        <span class="chip bg-color">Matlab</span>
                    </a>
                    
                </div>
                
            </div>
        </div>
        
        
        <div class="article col s12 m6" data-aos="fade-up">
            <div class="article-badge right-badge text-color">
                下一篇&nbsp;<i class="fas fa-chevron-right"></i>
            </div>
            <div class="card">
                <a href="/shier_jinghuang/2022/01/12/Matlab%E6%95%B0%E6%8D%AE%E5%A4%84%E7%90%86/">
                    <div class="card-image">
                        
                        
                        <img src="/shier_jinghuang/medias/featureimages/3.jpg" class="responsive-img" alt="Matlab数据处理">
                        
                        <span class="card-title">Matlab数据处理</span>
                    </div>
                </a>
                <div class="card-content article-content">
                    <div class="summary block-with-text">
                        
                            
                        
                    </div>
                    <div class="publish-info">
                            <span class="publish-date">
                                <i class="far fa-clock fa-fw icon-date"></i>2022-01-12
                            </span>
                        <span class="publish-author">
                            
                            <i class="fas fa-bookmark fa-fw icon-category"></i>
                            
                            <a href="/shier_jinghuang/categories/%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/" class="post-category">
                                    学习笔记
                                </a>
                            
                            
                        </span>
                    </div>
                </div>
                
                <div class="card-action article-tags">
                    
                    <a href="/shier_jinghuang/tags/%E5%AD%A6%E4%B9%A0%E8%AE%B0%E5%BD%95/">
                        <span class="chip bg-color">学习记录</span>
                    </a>
                    
                    <a href="/shier_jinghuang/tags/Matlab/">
                        <span class="chip bg-color">Matlab</span>
                    </a>
                    
                </div>
                
            </div>
        </div>
        
    </div>
</article>

</div>



<!-- 代码块功能依赖 -->
<script type="text/javascript" src="/shier_jinghuang/libs/codeBlock/codeBlockFuction.js"></script>


  <!-- 是否加载使用自带的 prismjs. -->
  <script type="text/javascript" src="/shier_jinghuang/libs/prism/prism.min.js"></script>


<!-- 代码语言 -->

<script type="text/javascript" src="/shier_jinghuang/libs/codeBlock/codeLang.js"></script>


<!-- 代码块复制 -->

<script type="text/javascript" src="/shier_jinghuang/libs/codeBlock/codeCopy.js"></script>


<!-- 代码块收缩 -->

<script type="text/javascript" src="/shier_jinghuang/libs/codeBlock/codeShrink.js"></script>



    </div>
    <div id="toc-aside" class="expanded col l3 hide-on-med-and-down">
        <div class="toc-widget card" style="background-color: white;">
            <div class="toc-title"><i class="far fa-list-alt"></i>&nbsp;&nbsp;目录</div>
            <div id="toc-content"></div>
        </div>
    </div>
</div>

<!-- TOC 悬浮按钮. -->

<div id="floating-toc-btn" class="hide-on-med-and-down">
    <a class="btn-floating btn-large bg-color">
        <i class="fas fa-list-ul"></i>
    </a>
</div>


<script src="/shier_jinghuang/libs/tocbot/tocbot.min.js"></script>
<script>
    $(function () {
        tocbot.init({
            tocSelector: '#toc-content',
            contentSelector: '#articleContent',
            headingsOffset: -($(window).height() * 0.4 - 45),
            collapseDepth: Number('0'),
            headingSelector: 'h2, h3, h4'
        });

        // Set scroll toc fixed.
        let tocHeight = parseInt($(window).height() * 0.4 - 64);
        let $tocWidget = $('.toc-widget');
        $(window).scroll(function () {
            let scroll = $(window).scrollTop();
            /* add post toc fixed. */
            if (scroll > tocHeight) {
                $tocWidget.addClass('toc-fixed');
            } else {
                $tocWidget.removeClass('toc-fixed');
            }
        });

        
        /* 修复文章卡片 div 的宽度. */
        let fixPostCardWidth = function (srcId, targetId) {
            let srcDiv = $('#' + srcId);
            if (srcDiv.length === 0) {
                return;
            }

            let w = srcDiv.width();
            if (w >= 450) {
                w = w + 21;
            } else if (w >= 350 && w < 450) {
                w = w + 18;
            } else if (w >= 300 && w < 350) {
                w = w + 16;
            } else {
                w = w + 14;
            }
            $('#' + targetId).width(w);
        };

        // 切换TOC目录展开收缩的相关操作.
        const expandedClass = 'expanded';
        let $tocAside = $('#toc-aside');
        let $mainContent = $('#main-content');
        $('#floating-toc-btn .btn-floating').click(function () {
            if ($tocAside.hasClass(expandedClass)) {
                $tocAside.removeClass(expandedClass).hide();
                $mainContent.removeClass('l9');
            } else {
                $tocAside.addClass(expandedClass).show();
                $mainContent.addClass('l9');
            }
            fixPostCardWidth('artDetail', 'prenext-posts');
        });
        
    });
</script>

    

</main>




    <footer class="page-footer bg-color">
    
        <link rel="stylesheet" href="/shier_jinghuang/libs/aplayer/APlayer.min.css">
<style>
    .aplayer .aplayer-lrc p {
        
        display: none;
        
        font-size: 12px;
        font-weight: 700;
        line-height: 16px !important;
    }

    .aplayer .aplayer-lrc p.aplayer-lrc-current {
        
        display: none;
        
        font-size: 15px;
        color: #42b983;
    }

    
    .aplayer.aplayer-fixed.aplayer-narrow .aplayer-body {
        left: -66px !important;
    }

    .aplayer.aplayer-fixed.aplayer-narrow .aplayer-body:hover {
        left: 0px !important;
    }

    
</style>
<div class="">
    
    <div class="row">
        <meting-js class="col l8 offset-l2 m10 offset-m1 s12"
                   server="netease"
                   type="playlist"
                   id="503838841"
                   fixed='true'
                   autoplay='false'
                   theme='#42b983'
                   loop='all'
                   order='random'
                   preload='auto'
                   volume='0.7'
                   list-folded='true'
        >
        </meting-js>
    </div>
</div>

<script src="/shier_jinghuang/libs/aplayer/APlayer.min.js"></script>
<script src="/shier_jinghuang/libs/aplayer/Meting.min.js"></script>

    

    <div class="container row center-align"
         style="margin-bottom: 0px !important;">
        <div class="col s12 m8 l8 copy-right">
            Copyright&nbsp;&copy;
            
                <span id="year">2019-2023</span>
            
            <a href="/shier_jinghuang/about" target="_blank">十二惊惶</a>
            |&nbsp;Powered by&nbsp;<a href="https://hexo.io/" target="_blank">Hexo</a>
            |&nbsp;Theme&nbsp;<a href="https://github.com/blinkfox/hexo-theme-matery" target="_blank">Matery</a>
            <br>
            
                &nbsp;<i class="fas fa-chart-area"></i>&nbsp;站点总字数:&nbsp;<span
                        class="white-color">289.6k</span>
            
            
            
                
            
            
                <span id="busuanzi_container_site_pv">
                &nbsp;|&nbsp;<i class="far fa-eye"></i>&nbsp;总访问量:&nbsp;
                    <span id="busuanzi_value_site_pv" class="white-color"></span>
            </span>
            
            
                <span id="busuanzi_container_site_uv">
                &nbsp;|&nbsp;<i class="fas fa-users"></i>&nbsp;总访问人数:&nbsp;
                    <span id="busuanzi_value_site_uv" class="white-color"></span>
            </span>
            
            <br>

            <!-- 运行天数提醒. -->
            
            <br>
            
        </div>
        <div class="col s12 m4 l4 social-link social-statis">
    <a href="https://github.com/blinkfox" class="tooltipped" target="_blank" data-tooltip="访问我的GitHub" data-position="top" data-delay="50">
        <i class="fab fa-github"></i>
    </a>



    <a href="mailto:1181062873@qq.com" class="tooltipped" target="_blank" data-tooltip="邮件联系我" data-position="top" data-delay="50">
        <i class="fas fa-envelope-open"></i>
    </a>







    <a href="tencent://AddContact/?fromId=50&fromSubId=1&subcmd=all&uin=1181062873" class="tooltipped" target="_blank" data-tooltip="QQ联系我: 1181062873" data-position="top" data-delay="50">
        <i class="fab fa-qq"></i>
    </a>







    <a href="/shier_jinghuang/atom.xml" class="tooltipped" target="_blank" data-tooltip="RSS 订阅" data-position="top" data-delay="50">
        <i class="fas fa-rss"></i>
    </a>

</div>
    </div>
</footer>

<div class="progress-bar"></div>


    <!-- 搜索遮罩框 -->
<div id="searchModal" class="modal">
    <div class="modal-content">
        <div class="search-header">
            <span class="title"><i class="fas fa-search"></i>&nbsp;&nbsp;搜索</span>
            <input type="search" id="searchInput" name="s" placeholder="请输入搜索的关键字"
                   class="search-input">
        </div>
        <div id="searchResult"></div>
    </div>
</div>

<script type="text/javascript">
$(function () {
    var searchFunc = function (path, search_id, content_id) {
        'use strict';
        $.ajax({
            url: path,
            dataType: "xml",
            success: function (xmlResponse) {
                // get the contents from search data
                var datas = $("entry", xmlResponse).map(function () {
                    return {
                        title: $("title", this).text(),
                        content: $("content", this).text(),
                        url: $("url", this).text()
                    };
                }).get();
                var $input = document.getElementById(search_id);
                var $resultContent = document.getElementById(content_id);
                $input.addEventListener('input', function () {
                    var str = '<ul class=\"search-result-list\">';
                    var keywords = this.value.trim().toLowerCase().split(/[\s\-]+/);
                    $resultContent.innerHTML = "";
                    if (this.value.trim().length <= 0) {
                        return;
                    }
                    // perform local searching
                    datas.forEach(function (data) {
                        var isMatch = true;
                        var data_title = data.title.trim().toLowerCase();
                        var data_content = data.content.trim().replace(/<[^>]+>/g, "").toLowerCase();
                        var data_url = data.url;
                        data_url = data_url.indexOf('/') === 0 ? data.url : '/' + data_url;
                        var index_title = -1;
                        var index_content = -1;
                        var first_occur = -1;
                        // only match artiles with not empty titles and contents
                        if (data_title !== '' && data_content !== '') {
                            keywords.forEach(function (keyword, i) {
                                index_title = data_title.indexOf(keyword);
                                index_content = data_content.indexOf(keyword);
                                if (index_title < 0 && index_content < 0) {
                                    isMatch = false;
                                } else {
                                    if (index_content < 0) {
                                        index_content = 0;
                                    }
                                    if (i === 0) {
                                        first_occur = index_content;
                                    }
                                }
                            });
                        }
                        // show search results
                        if (isMatch) {
                            str += "<li><a href='" + data_url + "' class='search-result-title'>" + data_title + "</a>";
                            var content = data.content.trim().replace(/<[^>]+>/g, "");
                            if (first_occur >= 0) {
                                // cut out 100 characters
                                var start = first_occur - 20;
                                var end = first_occur + 80;
                                if (start < 0) {
                                    start = 0;
                                }
                                if (start === 0) {
                                    end = 100;
                                }
                                if (end > content.length) {
                                    end = content.length;
                                }
                                var match_content = content.substr(start, end);
                                // highlight all keywords
                                keywords.forEach(function (keyword) {
                                    var regS = new RegExp(keyword, "gi");
                                    match_content = match_content.replace(regS, "<em class=\"search-keyword\">" + keyword + "</em>");
                                });

                                str += "<p class=\"search-result\">" + match_content + "...</p>"
                            }
                            str += "</li>";
                        }
                    });
                    str += "</ul>";
                    $resultContent.innerHTML = str;
                });
            }
        });
    };

    searchFunc('/shier_jinghuang/search.xml', 'searchInput', 'searchResult');
});
</script>

    <!-- 白天和黑夜主题 -->
<div class="stars-con">
    <div id="stars"></div>
    <div id="stars2"></div>
    <div id="stars3"></div>  
</div>

<script>
    function switchNightMode() {
        $('<div class="Cuteen_DarkSky"><div class="Cuteen_DarkPlanet"></div></div>').appendTo($('body')),
        setTimeout(function () {
            $('body').hasClass('DarkMode') 
            ? ($('body').removeClass('DarkMode'), localStorage.setItem('isDark', '0'), $('#sum-moon-icon').removeClass("fa-sun").addClass('fa-moon')) 
            : ($('body').addClass('DarkMode'), localStorage.setItem('isDark', '1'), $('#sum-moon-icon').addClass("fa-sun").removeClass('fa-moon')),
            
            setTimeout(function () {
            $('.Cuteen_DarkSky').fadeOut(1e3, function () {
                $(this).remove()
            })
            }, 2e3)
        })
    }
</script>

    <!-- 回到顶部按钮 -->
<div id="backTop" class="top-scroll">
    <a class="btn-floating btn-large waves-effect waves-light" href="#!">
        <i class="fas fa-arrow-up"></i>
    </a>
</div>


    <script src="/shier_jinghuang/libs/materialize/materialize.min.js"></script>
    <script src="/shier_jinghuang/libs/masonry/masonry.pkgd.min.js"></script>
    <script src="/shier_jinghuang/libs/aos/aos.js"></script>
    <script src="/shier_jinghuang/libs/scrollprogress/scrollProgress.min.js"></script>
    <script src="/shier_jinghuang/libs/lightGallery/js/lightgallery-all.min.js"></script>
    <script src="/shier_jinghuang/js/matery.js"></script>

    

    

    <!-- 雪花特效 -->
    

    <!-- 鼠标星星特效 -->
    

     
        <script src="https://ssl.captcha.qq.com/TCaptcha.js"></script>
        <script src="/shier_jinghuang/libs/others/TencentCaptcha.js"></script>
        <button id="TencentCaptcha" data-appid="xxxxxxxxxx" data-cbfn="callback" type="button" hidden></button>
    

    <!-- Baidu Analytics -->

    <!-- Baidu Push -->

<script>
    (function () {
        var bp = document.createElement('script');
        var curProtocol = window.location.protocol.split(':')[0];
        if (curProtocol === 'https') {
            bp.src = 'https://zz.bdstatic.com/linksubmit/push.js';
        } else {
            bp.src = 'http://push.zhanzhang.baidu.com/push.js';
        }
        var s = document.getElementsByTagName("script")[0];
        s.parentNode.insertBefore(bp, s);
    })();
</script>

    
    <script src="/shier_jinghuang/libs/others/clicklove.js" async="async"></script>
    
    
    <script async src="/shier_jinghuang/libs/others/busuanzi.pure.mini.js"></script>
    

    

    

    <!--腾讯兔小巢-->
    
    

    

    

    
    <script src="/shier_jinghuang/libs/instantpage/instantpage.js" type="module"></script>
    

</body>

</html>
